Almost “very strong” multilane turnpike effect in a non‑stationary Gale economy with a temporary von Neumann equilibrium and price constraints

Abstract

Mathematical models of economic dynamics and growth are usually expressed in terms of differential equations/inclusions (in the case of continuous time) or difference equations/inclusions (if discrete time is assumed).3 This class of models includes von Neumann-Leontief-Gale type dynamic input-output models to which the paper refers. The paper focuses on the turnpike stability of optimal growth processes in a Gale non-stationary economy with discrete time in the neighbourhood of von Neumann dynamic equilibrium states (so-called growth equilibrium). The paper refers to Panek (2019, 2020) and shows an intermediate result between the strong and very strong turnpike theorem in the non-stationary Gale economy with changing technology assuming that the prices of temporary equilibrium in such an economy (so-called von Neumann prices) do not change rapidly. The aim of the paper is to bring mathematical proof that the introduction of these assumptions making the model more realistic does not change its asymptotic (turnpike-like) properties.